What is 1 1/2 ÷ 5/6?

Steps to Solve

1. Convert the mixed fraction to an improper fraction

To convert $1 \frac{1}{2}$ to an improper fraction, multiply the whole number (1) by the denominator (2) and add the numerator (1). Then, place the result over the original denominator.

$1 \frac{1}{2} = \frac{(1 \times 2) + 1}{2} = \frac{2 + 1}{2} = \frac{3}{2}$

2. Rewrite the division problem

Now we can rewrite the original problem as:

$\frac{3}{2} \div \frac{5}{6}$

3. Multiply by the reciprocal

To divide by a fraction, we multiply by its reciprocal. The reciprocal of $\frac{5}{6}$ is $\frac{6}{5}$. So, we have:

$\frac{3}{2} \times \frac{6}{5}$

4. Multiply the numerators and the denominators

Multiply the numerators together and the denominators together:

$\frac{3 \times 6}{2 \times 5} = \frac{18}{10}$

5. Simplify the fraction

Simplify $\frac{18}{10}$ by dividing both the numerator and denominator by their greatest common divisor, which is 2:

$\frac{18 \div 2}{10 \div 2} = \frac{9}{5}$

6. Convert the improper fraction to a mixed fraction (optional)

If desired, convert the improper fraction $\frac{9}{5}$ to a mixed fraction. Divide 9 by 5:

$9 \div 5 = 1$ with a remainder of $4$.

So, $\frac{9}{5} = 1 \frac{4}{5}$